# Simplification Basic Concepts with Examples

Simplification is very easy and important topic according to banking, SSC and other govt. exam perspective. Simplification is based on basic math calculations and some other algebraic topics. Simplification is less time consuming and having higher accuracy.

Basic Topics on which Simplification is based on:
• BODMAS rules
• Approximation
• Percentage
• Squares
• Cubes.

### Simplification Tricks and Techniques:

Simplification is converting or finding the missing values from the long and complex expressions using the basic BODMAS rules where:
B → Stands for bracket and operation of brackets in the order ( ), { } and [ ]
O → Stands for ‘of’ (usage as ✕)
D → Stands for Division (/)

M → Stands for Multiplication (✕)
A → Stands for Addition (+)
S → Stands for Subtraction (-)

### Concept

1. Step 1: Solve for the expressions which are enclosed in Brackets like ( ), { } and [ ], inside the brackets using BODMAS rules.
2. Step 2: The mathematical operators like ‘of’ and ‘order’ must be solved next. Where ‘Of’ means part of and is solved by substituting with a multiplication sign. ‘Order’ is the same as an exponent. Powers are solved after brackets. Powers also include roots.
3. Step 3: Then the part of equation containing Multiplication and Division must be solved next from left to right
4. Step 4: Last but not least, the parts of the equation that contains ‘Addition’ and ‘Subtraction’ should be calculated which will provide us with the solution of complex expression or required value in expression

## Examples:

### 1. Solve for the question mark (?) in the following question?

1600 ÷ 32 – 5{5 ✕ 2(324 ÷ 90 ✕ 10)} + 89
SOLUTION:
Here in the expression, there is one curly bracket and round bracket. So we will first solve the expression enclosed in the round brackets using BODMAS rule
Here are the steps to illuminate this process.
⇒ 1600 ÷ 32 – 5{5 ✕ 2(3.6 ✕ 10)} + 89 = ?
⇒ 1600 ÷ 32 – 5{18 ✕ 2(36)} + 89 = ?
Now we will solve the curly bracket using the BODMAS rule within the bracket
Now solving curly bracket,
⇒ 1600 ÷ 32 – 5 {18 ✕ 2 ✕ 36} + 89 = ?
⇒ 1600 ÷ 32 – 5{360} + 89 = ?
Now we are done with the brackets and left with general mathematics expression. Now we will move to next step which is about division and multiplication. As both of this is of the same rank so we have to apply them from left to right as follows:
⇒ 1600 ÷ 32 – 5 ✕ 360 + 89= ?
⇒ 1600 ÷ 32 – 1800 + 89 = ?
⇒ 50 – 1800 + 89= ?
Now we are left with the last step which is about addition and subtraction and in this question we have both addition and subtraction so we will do that and we will left with our required answer
⇒? = - 1661
Hence, the required answer is - 1661.

### 2. Solve for the question mark (?) in the following question?

28 – 70 ÷ 14 ✕ 6 ✕ 4/3 of 10 + (63 ÷ 9) = ?
SOLUTION:
28 – 70 ÷ 14 ✕ 6 ✕ \frac {4}{3} of 10 + (7) = ?
28 – 70 ÷ 14 ✕ 6 ✕ \frac {4}{3} x 10 + (7) = ?
28 – 5 ✕ 6 ✕ \frac {4}{3} ✕ 10 + 7 = ?
28 – 400 + 7 = ?
? = -365

## Try out some Examples for Simplification

1. What will come in place of question mark (?) in the following question?

245 - 16 + 8 × \frac {1}{2} of 15 - {50 ÷ ((55 + 30 ÷ 3) ÷ 13)} =?

2. What will come in place of question mark (?) in the following question?

560 ÷ 8 × 128 ÷ 4 +\frac {1}{2} of {900 ÷ (6 × 48 ÷ 12 × 4 – 51)} =?

For Simplification we have to Remember some Basic things which can be applied easily and quickly:
1. Squares of number (1 to 30)
2. Cubes of number (1 to 15)
• 5 % = 0.05
• 6 \frac {1}{4} = 0.0625
• 10% = 0.10
• 12 \frac {1}{2} = 0.125
• 16 ✕ (\frac {2}{3})% = 0.166
• 20% = 0.2
• 25 % = 0.25
• 33 ✕ (\frac {1}{3})% = 0.33
• 40% = 0.4
• 50% = 0.5
• 60% = 0.6
• 75% = 0.75
• 80% = 0.8
• 90% = 0.9
• 100% = 1

## Examples:

### 1. 40% of 300 +30% of 700

STEP 1: Know the values of 40% =0.4 and 30 % = 0.3
STEP 2: Now directly multiply 0.4 × 300 + 0.3 × 700
STEP 3: 0.4 × 300 = 120, 0.3 × 700 = 210
STEP 4: 120 + 210 = 330
STEP 5: Hence the answer for above series is 330
Solve mixed fraction – Multiplication

### 2. 4 × (\frac {2}{5}) × 6 × (\frac {1}{2}) + 8 \frac {1}{2} × 3 × (\frac {1}{3})

STEP 1: 4 × (\frac {2}{5}) × 6 × (\frac {1}{2}) = (\frac {8}{5}) × (3) = \frac {24}{5}

STEP 2: + 8 \frac {1}{2} × 3 × (\frac {1}{3}) = \frac {17}{2} × 1 = \frac {17}{2}

STEP 3: \frac {24}{5} + \frac {17}{2} = \frac {133}{10} = 13.3

STEP 4: hence the answer for above series is 13.3

### 3. (?)^{2} +9 × 21 = 62 × 12 × 5

STEP 1: Multiply 9 × 21 = 189
STEP 2: Square of 6 = 36
STEP 3: Multiply 36 × 12 × 5= 2160
STEP 4: (X)^{2} +189 = 2160
STEP 5: (X)^{2} = 2160 - 189 = 1971
STEP 6: Therefore X = 44.4

### 4. Find the approximate value of the following question (8.96)^{3} – (20.99)^{2} + (2.983)^{5} = ?

Solution:
There is no need to calculate the exact value when asked about the approximate value and we can perfectly judge the answers through our options available in the question
(9)^{3} – (21)^{2} + (3)^{5} = ?
729 – 441 + 243 = ?
531 =?
= 530